Given this pair of slopes, what is the value of n if the lines are parallel? What is the value of n if the lines are perpendicular?

\({3 \over n}\),\(-{7 \over 2}\)

If I cross multiply, the parallel slope is \(n = -{6 \over 7}\), is that right?

As for perpendicular... how would I solve for that?

Guest Apr 8, 2018

#1**+3 **

Parallel lines have the same slope.

If the lines are parallel, then the slopes of the lines are equal.

If the lines area parallel, then....

\(\frac3n\,=\,-\frac72 \\~\\ 3\cdot2\,=\,-7\cdot n \\~\\ 6\,=\,-7n\\~\\ n\,=\,-\frac67\)

....You're right!!!

If the lines are perpendicular, then the slopes are negative reciprocals of each other.

That means \(\frac3n\) must equal the negative reciprocal of \(-\frac72\) .

The negative reciprocal of \(-\frac72\) is \(\frac27\) .

If the lines are perpendicular, then....

\(\frac3n\,=\,\frac27\\~\\ 7\cdot3\,=\,2\cdot n\\~\\ 21\,=\,2n\\~\\ n\,=\,\frac{21}{2}\)

hectictar
Apr 8, 2018